The dependence of the EPR of the plate on the angle formula. Effective scattering area. EPR of common point targets

It is customary to distinguish between specular, diffuse and resonant reflections. If the linear dimensions of the reflecting surface are much larger than the wavelength, and the surface itself is smooth, then a specular reflection occurs. In this case, the angle of incidence of the radio beam is equal to the angle of reflection, and the secondary radiation wave does not return to the radar (except in the case of normal incidence).

If the linear dimensions of the surface of the object are large compared to the wavelength, and the surface itself is rough, then diffuse reflection takes place. In this case, due to the different orientation of the surface elements, electromagnetic waves are scattered in different directions, including in the direction of the radar. Resonant reflection is observed when the linear dimensions of the reflecting objects or their elements are equal to an odd number of half-waves. Unlike diffuse reflection, secondary resonant radiation usually has a high intensity and a pronounced directionality, depending on the design and orientation of the reflecting element.

In cases where the wavelength is large compared to the linear dimensions of the target, the incident wave goes around the target and the intensity of the reflected wave is negligible.

From the point of view of signal formation upon reflection, objects of radar observation are usually divided into small-sized and distributed in space or on the surface.

Small-sized objects include objects whose dimensions are much smaller than the dimensions of the radar resolution element in terms of range and angular coordinates. In some cases, small-sized objects have the simplest geometric configuration. Their reflective properties can be easily determined theoretically and predicted for each specific relative location of the target in question and the radar. In real conditions, goals of the simplest type are quite rare. More often you have to deal with objects of complex configuration, which consist of a number of rigidly interconnected simple reflective elements. Aircraft, ships, various structures, etc. can serve as examples of targets of complex configuration.

Other targets are a collection of individual objects distributed in a certain area of space, much larger than the resolution element of the radar. Depending on the nature of this distribution, volume-distributed (for example, a rain cloud) and surface-distributed (land surface, etc.) targets are distinguished. The signal reflected from such a target is the result of the interference of reflector signals distributed within the resolution bin.

For a fixed relative position of the radar and reflecting objects, the amplitude and phase of the reflected wave have a well-defined value. Therefore, in principle, the resulting total reflected signal can be determined for each specific case. However, during radar surveillance, the relative positions of the targets and the radar usually change, resulting in random fluctuations in the intensity and phase of the resulting echoes.

Effective target scattering area (ESR).

The calculation of the range of radar observation requires a quantitative characteristic of the intensity of the reflected wave. The power of the reflected signal at the input of the station receiver depends on a number of factors and, above all, on the reflecting properties of the target. Typically, radar targets are characterized by an effective scattering area. Under the effective scattering area of the target in the case when the radar antenna radiates and receives electromagnetic waves of the same polarization, it is understood the value σt, which satisfies the equation σtP1=4πK2P2, where P1 is the power flux density of the direct wave of this polarization at the target location; P2 is the power flux density of a wave of a given polarization reflected from the target at the radar antenna; R is the distance from the radar to the target. The RCS value can be directly calculated by the formula

σcP1=4πR2P2/ P1

As follows from the formula above, σц has the dimension of area. Therefore, it can be conditionally considered as a certain area equivalent to the target, normal to the radio beam, with area σц, which, isotropically scattering all the wave power incident on it from the radar, creates at the receiving point the same power flux density P2 as the real target.

If the RCS of the target is given, then with known values of P1 and R, it is possible to calculate the power flux density of the reflected wave P, and then, having determined the power of the received signal, estimate the range of the radar station.

The effective scattering area σc does not depend on the intensity of the emitted wave, nor on the distance between the station and the target. Indeed, any increase in P1 leads to a proportional increase in P2, and their ratio in the formula does not change. When changing the distance between the radar and the target, the ratio P2/P1 changes inversely proportional to R2 and the value of σc remains unchanged.

Complex and group goals

Consideration of the simplest reflectors does not cause difficulties. Most real radar targets are a complex combination of different types of reflectors. In the process of radar observation of such targets, one deals with a signal that is the result of the interference of several signals reflected from individual elements of the target.

When a complex object is irradiated (for example, an aircraft, a ship, a tank, etc.), the nature of the reflections from its individual elements strongly depends on their orientation. In some positions, certain parts of the aircraft or ship may produce very intense signals, and in other positions, the intensity of the reflected signals may drop to zero. In addition, when the position of the object relative to the radar changes, the phase relationships between the signals reflected from various elements change. This results in fluctuations in the resulting signal.

Other reasons for changes in the intensity of the reflected signals are also possible. Thus, there may be a change in conductivity between the individual elements of the aircraft, one of the causes of which are vibrations caused by the operation of the engine. When the conductivity changes, the distributions of the currents induced on the aircraft surface and the intensity of the reflected signals change. For propeller and turboprop aircraft, an additional source of change in the intensity of reflections is the rotation of the propeller.

Fig 2.1. Dependence of the RCS of the target on the angle.

In the process of radar observation, the mutual position of the aircraft (ship) and the radar is constantly changing. The result of this is the fluctuations of the reflected signals and the corresponding changes in the EPR. The laws of probability distribution of the effective scattering area of the target and the nature of changes in this value over time are usually determined experimentally. To do this, the intensity of the reflected signals is recorded and, after processing the record, the statistical characteristics of the signals and EPR are found.

As many studies have shown, the exponential distribution law is valid with sufficient accuracy for the fluctuation σc of aircraft

EPR has the dimensions of the area, but is not a geometric area, but is an energy characteristic, that is, it determines the magnitude of the power of the received signal.

The RCS of the target does not depend on the intensity of the emitted wave, nor on the distance between the station and the target. Any increase in ρ 1 leads to a proportional increase in ρ 2 and their ratio in the formula does not change. When changing the distance between the radar and the target, the ratio ρ 2 / ρ 1 changes inversely proportional to R and the EPR value remains unchanged.

EPR of common point targets

For most point targets, information about the EPR can be found in radar manuals.

convex surface

The field from the entire surface S is determined by the integral It is necessary to determine E 2 and the ratio at a given distance to the target ...

where k is the wave number.

1) If the object is small, then the distance and field of the incident wave can be considered unchanged. 2) The distance R can be considered as the sum of the distance to the target and the distance within the target:

,
,
,
,

flat plate

A flat surface is a special case of a curvilinear convex surface.

Corner reflector

The principle of operation of the corner reflector

Corner reflector consists of three perpendicular surfaces. Unlike a plate, a corner reflector gives good reflection over a wide range of angles.

Triangular

If a corner reflector with triangular faces is used, then the EPR

Application of corner reflectors

Corner reflectors are applied

as decoys
like radio contrast landmarks
when conducting experiments with strong directional radiation

chaff

Chaffs are used to create passive interference with the operation of the radar.

The value of the RCS of a dipole reflector generally depends on the observation angle, however, the RCS for all angles:

Chaffs are used to mask air targets and terrain, as well as passive radar beacons.

The reflection sector of the chaff is ~70°

EPR of complex targets

RCS of complex real objects are measured at special installations, or ranges, where the conditions of the far irradiation zone are achievable.

#	Target type	σ c
1	Aviation
1.1	Fighter aircraft	3-12
1.2	stealth fighter	0,3-0,4
1.3	frontline bomber	7-10
1.4	Heavy bomber	13-20
1.4.1	B-52 bomber	100
1.4	Transport aircraft	40-70
2	ships
2.1	Submarine on the surface	30-150
2.2	Cutting a submarine on the surface	1-2
2.3	small craft	50-200
2.4	medium ships	²
2.5	big ships	> 10²
2.6	Cruiser	~12 000 14 000
3	Ground targets
3.1	Automobile	3-10
3.2	Tank T-90	29
4	Ammunition
4.1	ALSM cruise missile	0,07-0,8
4.2	The warhead of an operational-tactical missile	0,15-1,6
4.3	ballistic missile warhead	0,03-0,05
5	Other purposes
5.1	Human	0,8-1
6	Birds
6.1	Rook	0,0048
6.2	mute swan	0,0228
6.3	Cormorant	0,0092
6.4	red kite	0,0248
6.5	Mallard	0,0214
6.6	Grey goose	0,0225
6.7	Hoodie	0,0047
6.8	field sparrow	0,0008
6.9	common starling	0,0023
6.10	black-headed gull	0,0052
6.11	White stork	0,0287
6.12	Lapwing	0,0054
6.13	Turkey vulture	0,025
6.14	rock dove	0,01
6.15	house sparrow	0,0008

The simplest volumetrically distributed targets are chaff, which are dropped in large numbers from an aircraft or fired by special projectiles, disperse in the air and form a cloud of reflectors. They are used to set up passive interference in a wide frequency range and simultaneously against many RTS.

Chaff are passive half-wave vibrators with a geometric length close to half the wavelength of the irradiating radar (l ≈ 0.47λ). They are made from metallized paper, aluminum foil, metallized fiberglass and other materials.

EPR clouds from n chaff reflectors is determined by the product of the RCS of individual reflectors located in the cloud:

σ = n σ do,

Where: σ do– EPR of one dipole reflector.

With linear polarization of the incident electromagnetic wave, the maximum value of the RCS of a single dipole reflector is observed when its geometric axis coincides with the vector E strength of the electric field of the wave. Then:

σ do max = 0.86λ 2

If the chaff is oriented perpendicular to the vector E irradiating electromagnetic wave, then σ do = 0.

Due to the turbulence of the atmosphere and the difference in the aerodynamic properties of dipole reflectors, they orient themselves randomly in the cloud. Therefore, the average value of the RCS of a single dipole reflector is used in calculations.

σ do sr = 1/5 σ do max = 0.17λ 2,

Where: λ - wavelength of the irradiating radar.

It follows that the simultaneous suppression of RTS operating at different frequencies is possible only when using chaff of different lengths.

The simplest point targets are corner reflectors. With relatively small geometric dimensions, they have a significant RCS in a wide range of wavelengths, which makes it possible to effectively simulate various point targets.

Corner reflector consists of rigidly interconnected mutually perpendicular planes. The simplest corner reflector is a dihedral or trihedral angle (Fig. 3.3, a, b).

Fig.3.3. The principle of operation of the corner reflector:

A - dihedral; b - trihedral.

The trihedral corner reflector has the property of specular reflection towards the radar when irradiated within an angle of 45 0 , which ensures the preservation of a large RCS within this angle. To expand the scattering diagram, corner reflectors are used, consisting of four or eight corners. The DR of a trihedral reflector is shown in Fig. 3.4.

Fig.3.4. Scattering diagram of a trihedral reflector.

In practice, triangular corner reflectors are used, having a triangular, rectangular or sector shape (Fig. 3.5, a, b, c).

Fig.3.5. Corner reflectors: A - with triangular faces (θ 0.5 ≈ 60 0);

b - with sector faces; V - with square faces (θ 0.5 ≈ 35 0).

For objects of a simple geometric shape, analytical expressions can be obtained to determine their RCS. Since the power flux density is directly proportional to the square of the electric field strength, the EPR formula of the target can be represented as

σ \u003d 4πD 2 E 2 2 / E 2 1

Attitude E 2 / E 1, included in this expression, can be found on the basis of the Huygens principle. This method consists in that each point on the surface of the irradiated object is considered as a source of a secondary spherical wave. Then, summing up the action of secondary spherical waves at the location of the radar station, one can find the strength of the resulting electric field of the secondary radiation. Calculation formulas for determining the RCS of some simple targets are given in Table 3.1.

Table 3.1. EPR of some simple targets.

course project

SPbGUT im. Bonch-Bruevich

Department of Radio Systems and Signal Processing

Course project by discipline

"Radio systems", on the topic:

"Effective Scattering Area"

Completed:

Student of the RT-91 group

Krotov R.E.

Received by: professor of the department of ROS Gurevich V.E.

Quest issued: 10/30/13

Protection period: 12/11/13

Introduction and so on

Structural diagram of the radar

Schematic diagram of the radar

Theory of device operation

Conclusion

Bibliography

Effective scattering area

(EPR; eng. Radar Cross Section.RCS; in some sources effective scattering surface, effective scattering cross section,effective reflective area, EOP) in radar - the area of some fictitious flat surface located normally to the direction of the incident plane wave and being an ideal and isotropic re-radiator, which, when placed at the target location, creates the same power flux density at the radar station antenna as the real target .

Example of a monostatic EPR diagram (B-26 Invader)

RCS is a quantitative measure of the property of an object to scatter an electromagnetic wave. Along with the energy potential of the transceiver path and the CG of the radar antennas, the EPR of the object is included in the radar range equation and determines the range at which an object can be detected by radar. An increased RCS value means a greater radar visibility of an object, a decrease in RCS makes it difficult to detect (stealth technology).

The EPR of a particular object depends on its shape, size, material from which it is made, on its orientation (view) in relation to the antennas of the transmitting and receiving positions of the radar (including the polarization of electromagnetic waves), on the wavelength of the probing radio signal. The RCS is determined in the conditions of the far zone of the scatterer, the receiving and transmitting antennas of the radar.

Since RCS is a formally introduced parameter, its value does not coincide with either the value of the total surface area of the scatterer or the value of its cross-sectional area (eng. Cross section). Calculation of EPR is one of the problems of applied electrodynamics, which is solved with varying degrees of approximation analytically (only for a limited range of simple-shaped bodies, for example, a conducting sphere, cylinder, thin rectangular plate, etc.) or numerical methods. Measurement (control) of RCS is carried out at test sites and in radio frequency anechoic chambers using real objects and their scale models.

EPR has the dimension of area and is usually indicated in sq.m. or dBq.m.. For objects of a simple form - test - EPR is usually normalized to the square of the wavelength of the probing radio signal. EPR of extended cylindrical objects is normalized to their length (linear EPR, EPR per unit length). The EPR of objects distributed in the volume (for example, a rain cloud) is normalized to the volume of the radar resolution element (EPR / m3). The RCS of surface targets (as a rule, a section of the earth's surface) is normalized to the area of the radar resolution element (EPR / sq. M.). In other words, the RCS of distributed objects depends on the linear dimensions of a particular resolution element of a particular radar, which depend on the distance between the radar and the object.

EPR can be defined as follows (the definition is equivalent to that given at the beginning of the article):

Effective scattering area(for a harmonic probing radio signal) - the ratio of the radio emission power of an equivalent isotropic source (creating the same radio emission power flux density at the observation point as the irradiated scatterer) to the power flux density (W/sq.m.) of the probing radio emission at the location of the scatterer.

The RCS depends on the direction from the scatterer to the source of the probing radio signal and the direction to the observation point. Since these directions may not coincide (in the general case, the source of the probing signal and the point of registration of the scattered field are separated in space), then the RCS determined in this way is called bistatic EPR (two-position EPR, English bistatic RCS).

Backscatter diagram(DOR, monostatic EPR, single position EPR, English monostatic RCS, back-scattering RCS) is the RCS value when the directions from the scatterer to the source of the probing signal and to the observation point coincide. EPR is often understood as its special case - monostatic EPR, that is, DOR (the concepts of EPR and DOR are mixed) due to the low prevalence of bistatic (multi-position) radars (compared to traditional monostatic radars equipped with a single transceiver antenna). However, one should distinguish between EPR(θ, φ; θ 0, φ 0) and DOR(θ, φ) = EPR(θ, φ; θ 0 =θ, φ 0 =φ), where θ, φ is the direction to point of registration of the scattered field; θ 0 , φ 0 - direction to the source of the probing wave (θ, φ, θ 0 , φ 0 - angles of the spherical coordinate system, the beginning of which is aligned with the diffuser).

In the general case, for a probing electromagnetic wave with a non-harmonic time dependence (broadband probing signal in the space-time sense) effective scattering area is the ratio of the energy of an equivalent isotropic source to the energy flux density (J/sq.m.) of probing radio emission at the location of the scatterer.

EPR calculation

Consider the reflection of a wave incident on an isotropically reflecting surface with an area equal to the RCS. The power reflected from such a target is the product of the RCS and the density of the incident power flux:

where is the RCS of the target, is the power flux density of the incident wave of a given polarization at the target location, is the power reflected by the target.

On the other hand, the isotropically radiated power

Or, using the field strengths of the incident wave and the reflected wave:

Receiver input power:

where is the effective area of the antenna.

It is possible to determine the power flux of the incident wave in terms of the radiated power and the directivity of the antenna D for a given direction of radiation.

Where .

Thus,

. (9)

The physical meaning of epr

EPR has the dimension of area [ m²], But is not a geometric area(!), but is an energy characteristic, that is, it determines the magnitude of the power of the received signal.

The RCS of the target does not depend on the intensity of the emitted wave, nor on the distance between the station and the target. Any increase leads to a proportional increase and their ratio in the formula does not change. When changing the distance between the radar and the target, the ratio changes inversely and the RCS value remains unchanged.

EPR of common point targets

convex surface

Field from the entire surface S is determined by the integral It is necessary to determine E 2 and attitude at a given distance to the target ...

Where k- wave number.

1) If the object is small, then the distance and field of the incident wave can be considered unchanged.

2) Distance R can be thought of as the sum of the distance to the target and the distance within the target:


,

,

flat plate

A flat surface is a special case of a curved convex surface.

Corner reflector

Corner reflector- a device in the form of a rectangular tetrahedron with mutually perpendicular reflective planes. The radiation that enters the corner reflector is reflected in the strictly opposite direction.

Triangular

If a corner reflector with triangular faces is used, then the EPR

chaff

Chaffs are used to create passive interference with the operation of the radar.

The value of the RCS of a dipole reflector generally depends on the observation angle, however, the RCS for all angles:

Chaffs are used to mask aerial targets and terrain, as well as passive radar beacons.

The reflection sector of the chaff is ~70°

Keywords

EFFECTIVE SCATTERING SURFACE / BALLISTIC OBJECT / RADAR REFLECTOR/ EFFECTIVE SURFACE SCATTERING / BALLISTIC OBJECT / RADAR REFLECTOR

annotation scientific article on electrical engineering, electronic engineering, information technology, author of scientific work - Akinshin Ruslan Nikolaevich, Bortnikov Andrey Alexandrovich, Tsybin Stanislav Mikhailovich, Mamon Yuri Ivanovich, Minakov Evgeny Ivanovich

To reduce the cost of full-scale testing of the reflective properties of simulators ballistic objects(BO) it is expedient to develop a model and an algorithm for calculating such radar objects. As a simulator ballistic objects complex is chosen radar reflector, made of a lossless dielectric in the form of a spherical Luneberg lens coated with a highly electrically conductive alloy, as well as a truncated cone, disk and cylindrical elements. Stages of the aperture version of reflection from the inner surface of the Luneberg lens are proposed. A physical model of reflection on structural elements and a modeling technique with a calculation algorithm have been developed effective scattering surface. An algorithm for calculating the resonant effective scattering surface ballistic objects. This algorithm is presented in graphical form. The interface of the computer complex is presented. As a simulator ballistic object selected difficult radar reflector, made of a lossless dielectric in the form of a sphere coated with a highly conductive alloy, as well as a truncated cone, disk and cylindrical elements. Comparative indicatrices of the simulator are graphically presented ballistic objects. A conclusion is drawn from a comparative analysis of the results of measurements in natural conditions and the results of modeling. Examples of numerical calculations of the RCS of the warhead of a BO simulator with an increased RCS and an increased all-angle view are given. Variants of warheads of the BO simulator with increased EPR and increased all-angle view with optimal placement of a radar dielectric reflector and a corner block with a sectional placement of dielectric reflectors were studied.

The text of the scientific work on the topic "Model and algorithm for calculating the effective scattering area of a simulator of a radar object"

Vol. 20, no. 06, 2017

RADIO ENGINEERING AND COMMUNICATIONS

UDC 621.396.96

DOI: 10.26467/2079-0619-2017-20-6-141-151

MODEL AND ALGORITHM FOR CALCULATION OF THE EFFECTIVE SCATTERING AREA OF A RADAR OBJECT SIMULATOR

R.N. Akinshin1, A.A. BORTNIKOV2, S.M. TSYBIN2, Yu.I. MAMON2, E.I. MINAKOV3

1 Section of Applied Problems, Russian Academy of Sciences, Moscow, Russia, 2 Central Design Bureau of Apparatus Engineering, Tula, Russia 3 Tula State University, Tula, Russia

To reduce the cost of full-scale testing of the reflective properties of simulators of ballistic objects (BO), it is advisable to develop a model and an algorithm for calculating the effective scattering surface of such radar objects. A complex radar reflector made of a lossless dielectric in the form of a spherical Luneberg lens coated with a highly electrically conductive alloy, as well as a truncated cone, a disk, and cylindrical elements is chosen as a simulator of ballistic objects. Stages of the aperture version of reflection from the inner surface of the Luneberg lens are proposed. A physical model of reflection on structural elements and a modeling technique with an algorithm for calculating the effective scattering surface have been developed. An algorithm for calculating the resonant effective scattering surface of ballistic objects has been developed. This algorithm is presented in graphical form. The interface of the computer complex is presented. As a simulator of a ballistic object, a complex radar reflector made of a lossless dielectric in the form of a sphere coated with a highly electrically conductive alloy, as well as a truncated cone, a disk, and cylindrical elements was chosen. Comparative indicatrices of the simulator of ballistic objects are presented graphically. A conclusion is drawn from a comparative analysis of the results of measurements in natural conditions and the results of modeling. Examples of numerical calculations of the RCS of the warhead of a BO simulator with an increased RCS and an increased all-angle view are given. Variants of warheads of the BO simulator with increased EPR and increased all-angle view with optimal placement of a radar dielectric reflector and a corner block with a sectional placement of dielectric reflectors were studied.

Key words: effective scattering surface, ballistic object, radar reflector.

INTRODUCTION

To reduce the cost of full-scale testing of the reflective properties of ballistic object (BO) simulators, it is advisable to develop a model and algorithm for calculating the effective scattering surface (ESR) of such radar objects. A complex radar reflector made of a lossless dielectric in the form of a spherical Luneberg lens coated with a highly electrically conductive alloy, as well as a truncated cone, a disk, and cylindrical elements was chosen as a BR simulator.

The aperture version of reflection from the inner surface of the Luneberg lens in a limited volume of a ballistic object model, taking into account the polarization of the incident wave and the lossless transmission coefficient through the dielectric, includes several stages.

STAGES OF THE APERTURE VARIANT OF REFLECTION FROM THE INTERNAL SURFACE

At the first stage, the wave runs onto the surface of the dielectric sphere R with a flux density S, wavelength X from a radar station (RLS), as a result of which the wave is polarized and deviates from the normal to the surface n by an angle t.

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Vol. 20, no. 06, 2017

The maximum tension E t in the lens develops at the boundary of the transition from the air medium to the dielectric, which is explained by a decrease in the wave resistance of the dielectric medium.

The second stage begins from the moment of passage through the dielectric zone 2R = 4, e = 3, 5 = 0.001 and is associated with a decrease in the coherent component of the strength.

The third stage begins from the moment of falling onto the inner surface of a sphere with a central angle φ = 1800, R = 50 mm, coating thickness 5 = 6 μm, where the dielectric-metal interface becomes a secondary source of radiation (Fig. 1).

Scattering from BO is described by a system of recurrent differential equations for an incoherent radar field.

dch(f) 1 frY ... j .

1 - I h0 (f) = keF,

dCh (f) + 1 f Г ] 4 (f) = 0,

df2 4k neg (lJ Y J

e 2 Ei (r) , Y N0 E0 (r) =

dg2 vC J X tg ^disl

e 2 E0 (r) , fl N0 E0 (r) =

dg2 1 C J X tg diesel

d(pm 1n e) dE (f, r)

| 0 - inside the cavity, Ii - outside;

where n is the number of elements.

Rice. Fig. 1. Passage of a beam in a spherical Luneberg lens 1. Passing of a beam in a spherical lens of Lyuneberg

Vol. 20, no. 06, 2017

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Boundary conditions on the surface with air

a (E.-E ") \u003d -T1G "(3)

where a is the conductivity of the environment; Ex - tension on x; E3 - tension on the surface £; x - specific coefficient of electrical conductivity.

Boundary conditions on the surface BS of the contact of the radar field with the layers of the structure

I (E0 - E1) = -x dE, (4)

where 5 is the depth of penetration of the wave into the metal; E0 - coherent component of the intensity; E1 - incoherent component of tension; x - specific coefficient of electrical conductivity in the layer; E is the total coherent and incoherent component of the field strength.

Boundary conditions for the EPR lens at 00

A! (0) = n(R + R)2 ctr, (5)

where R1 is the radius of the front hemisphere of the lens; I 2 - the radius of the rear hemisphere of the lens; kotr - coefficient of reflection from the surface of the lens.

Boundary conditions for the disk at 3600

a (3600) = n(Yadn) kotr, (6)

where I am - bottom radius; to neg. - coefficient of reflection from the bottom. Radiation conditions for the right side of the system (1), (2)

We represent the radar field in the form

E \u003d [s ] (E) \u003d | ^, N, Kk ] \u003d<

E0 + Ei E0 + Ei E0 + E1

where N, N, Nk - shape function at the nodes of finite elements (FE).

The mathematical description of the processes under consideration is presented using a system of two interrelated functionals:

Loss functional Фп (Е(г));

Scattering functional Φ (a(r)). Let us write the loss functional for the problem in the form

CM1 Aulayop High Technologies f "=/12 2

Vo1. 20, N0. 06, 2017

4p/a(E7 - Ex)c1£

- / O (E0 - Ex) + / k (1 - dt,

where E1 is the strength of the incoherent field; Eo - intensity of the coherent field; r - radial coordinate; x - coefficient of specific conductivity; в± - dielectric permittivity; ^01 - field intensity; k - scaling factor; yo is the coefficient of transmission through the dielectric; N0 - refractive index; bp - loss factor.

Let us write the scattering functional in the form

4zhkogo /F1

e(E12 + Eo2/E1)(C08ff 7 + 8Shff)

where a 1 - EPR incoherent field; a0 - EPR of the coherent field; f1 - angular coordinate; k0 - interference coefficient; Ф1 - unit surface function; kotr - reflection coefficient; Emax - maximum field strength; f| is the polarization angle for the wave.

By using the well-known finite element method relations for (9) and (10), matrix equations can be determined.

The conductivity matrix has the form

[k1] \u003d \ x [in] [In]

where x is the conductivity coefficient;

[B]t is the transposed gradient matrix of the shape function; £1 - surface area of CE with coating. The reflection matrix has the form

K 2 \u003d / Kotr N

where kotr - reflection coefficient; N is the transposed shape function matrix; 82 - by -

surface area of the CE.

The transmission matrix has the form

K3 \u003d R01 / y 0kMg W£3,

where y0 is the coefficient of transmission through the dielectric; k - scaling factor; ^ 01 - intensity of the radiated field from the primary source; £3 - surface area of the CE for the dielectric.

Vol. 20, W. 06, 2017

The refraction matrix has the form

where Yu is the frequency of the secondary radiation; c is the speed of light; 5о is the surface area of the CE of the secondary source.

Let us finally write the scattering matrix in the form

Kp = at U(kr) V02 (K1 + K0 - K2 + K3

where am is the EPR asymptote; u(kg) is the energy scattering function; Vo is the attenuation function on scattering elements.

Recurrent matrix systems for a radar field with boundary conditions can be written as

K "faH;, K1(E1)+K0(E0)=f; K (CTl) = 0, K1(E) + K0(E0) = 0,

fen = f NT (1 - q01)kQdV,

Here P0 is the wave resistance of air; k - interference coefficient; £1 - power flow from the secondary source (lens); qol is the intensity of the radiated field from the primary source (radar); n is the boundary distance to the lens; r11 is the distance along the BO aperture with the lens; φ is the angle of irradiation of the BO; Et - maximum field strength from the radar; d0 is the dielectric constant of air; /a0 - magnetic permeability of air.

ALGORITHM FOR CALCULATION OF THE RESONANT EFFECTIVE SCATTERING AREA

The algorithm for calculating the resonant EPR of the BO is shown in fig. 2.

To calculate the resonant RCS of inhomogeneous structures of the BO, an interface is implemented, consisting of three panels, in the first one the BO is visualized, and in the second a set of geometric and radar parameters is implemented, in the third there are tables of tabulated values of the results of experimental measurements and the current values of the calculation results and dependency graphs (Fig. 3 ).

Comparative indicatrices of BO, which are used to estimate the probability of detection, the number of BO simulators during testing, are shown in Fig. 4 . The numbers of indicatrices correspond to: 1 - with a spherical reflector (in anechoic conditions); 2nd reflector 1 and a block of corner reflectors (in anechoic conditions); 3 - reflector 1 and a block of corner reflectors (in natural conditions).

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Vol. 20, no. 06, 2017

Axial section coordinate

Dia<>m)_

Length of FE or FE from the origin (mm)

Central uhp in plan Ü (zpaö)

Coating thickness & _(µm)_

Coating pitch h

Number of layers and

Conductivity % (1 /s)

■ty-passage, go-intense stb. üi?TpaHt.

Kozf ficients

JVo-refraction Ki-interference

K - scaling, Ii - losses

1. Entering variable parameters

Frequency F-rank of the wave - 3. (cas)% tajstr antenna - D (aï)

U. Calculation of dpl of FE matrices and r-prop. frequencies

1U. Explanation for FE matrices and -m-prop. frequencies

b. The choice of EPR from tabup. tab. I

14. |sh-a|<5 i

13. Whispering!* system matrices

11. Combining KEiSE into the system

3. Calculation of psrameproe: DND, efficiency - g EPR \ suzazhnost - Q Vq L&

tfl, j^oi ^enz

Axial section coordinate

Axial section coordinate _DlS-mm)_

FE or SE length (aim)

Specific gravity or mass (kg / m?), (kg)

Generation of a set of finite impulses

Applying a FE mesh or thickening it

Accounting for additional conditions

Single and normal surfaces. funkt. F1 and F^

15. Displaying results

12. Accounting for boundary conditions

Rice. Fig. 2. Algorithm for calculating the resonant EPR of the BO 2. Algorithm of calculation of resonant EPR BO

J 50 Ptt"*.- 1"

Dh-1+n TlillWJi

| 30 Rshr * "« | ÖJ YAGCHmn

GddtrL.ii |30 PjWTprp.ifrt |s0

SMH# [EOO |TOO m

Display of secondary information

Tabulated EPR scattering indicatrix

EPR.m2 1.35 0.2 0.19

EPR scattering indicatrix

Radar operating modes

6 | 7 | 8 | 3 | 1P[

10.007 |a04 |0.02 |0.02

G Viewfinder G 0....3G0 G 0...90

With Impulse G One. C~ Group.

100 150 200 250 300 350

Radar parameters

Frequency, GHz | 10

Wavelength, cm h

Aperture.m2 10.046

Rice. Fig. 3. Computer complex interface: a - BO visualization; b - geometric and radar parameters; c - tables of tabulated values of experimental measurement results and current values of calculation results 3. Interface of the computer system: a) visualization of BO; b) geometrical and radar parameters; c) tables of the tabulated values of results of the experimental samplings and the current values of results of computation

Vol. 20, no. 06, 2017

Ovil Aviation High Technologies

Rice. Fig. 4. Comparative indicatrices of the BO simulator 4. Comparative indikatrisa of the BO simulator

A comparative analysis of the results of measurements in natural conditions and the results of simulation shows that the simulation error does not exceed 3 dB.

In order to improve the process of formation of the EPR of BO, taking into account the resonant frequency, the parabolic equation method was modified. The modification led to the determination of the effective area, taking into account the resonance on the radar reflective system (spherical dielectric reflector and block of corner reflectors). The finite element method (FEM) was chosen as a numerical method. It is assumed that the model takes into account the polarization of the wave and the anechoic conditions . The use of the FEM leads to an increase in the computation time with a decrease in the size of the elements and an increase in their number, namely, the number of transverse partitions in the corner block, passing to resonance phenomena, which imposes conditions on the solution of differential equations in partial derivatives for an incoherent field in parallel || and perpendicular to L

direction of radiation on the system det = 0 . Considering the foregoing, the calculated and

the measured scattering indicatrices are preferably tabulated in such a way that the angular step is equal to 10° and varies uniformly from 0 to 3600, while the amplitude values are output in such a way that it is convenient to calculate the scaling factor. Numerical studies of EPR were carried out taking into account the resonance according to the developed model depending on the angle of irradiation with and without a fiberglass fairing. The research results (Fig. 4) show that the RCS of the warhead (HF) of the BO simulator already significantly increases at irradiation angles from 10 to 80°, and at irradiation angles from 80 to 130°, the required value is actually provided by a highly electrically conductive coating . The amplitude of the main lobes at 90 and 270° is 3.8 m2, respectively, without a corner block, and at an irradiation angle of 0°, it is 2 m2 and, respectively, without a block, 1.35 m2.

Scientific Bulletin of MSTU GA_Volume 20, No. 06, 2017

Civil Aviation High Technologies Vol. 20, no. 06, 2017

The approximating polynomials of the EPR indicatrix of the BO simulator, obtained from the experiment and calculated using the developed model, are presented in Table. 1 and 2.

Table 1

1°-4° 81° 6r 4m - 0.0007c3m + 0.0206r2m + °.2611rm + 1.35;

2 4°-9° 51°-6st4t - 0.0013a3t + 0.121 g2t + 4.8181 gt + 71.42;

3 9°-13° 110-5r4 t - 0.0063 g3t + 1.071 g2 t - 80.487gt + 2261.5;

4 13°-17° -110 5g 4t + 0.0072s3t - 1.5851 g2t + 154.39st - 5619.7;

5 17°-19° -0.0057g2t + 2.059gt - 185.07;

6 19°-23° -910-6s4t + 0.0079g3t - 2.527s2t + 359.62gt - 19149;

7 23°-26° -910-7s4t + 0.0008g3t - 0.28g2t + 44.532gt - 2581.6;

8 26°-28° -0.026g2t + 14.036gt - 1891.4;

9 28°-31° 0.0009g2t - 0.5557gt + 82.653;

1° 31°-34° 0.0017g2 t - 1.1205 gt + 185.07;

11 34°-36° 1.0252 GT + 1.1819;

Table 2

No. Angular direction, deg Approximating polynomials (envelope) gt, m2

1°-4° 210-6r4 t - 0.0001 g3t + 0.0012r2 t + °.0°19gt - 1.39;

2 4°-9° 110-5r4 t - 0.0025 g3t + 0.2352 g2 t - 9.6315 gt + 145.52;

3 9°-13° -2 105 g4 t + 0.0109 g3t - 1.8145 g2 t + 132.81 gt + 3613

4 13°-17° -6 1°-6g4t + 0.0038g3t - 0.8712g2t + 89.711 gt - 3456.7

5 17°-19° -8 10-6 gt + 1.47

6 19 ° -23 ° -310 "6g4 t - 0.0024 g3t + 0.7664 g2 t - 1 ° 8.22gt + 5721.8

7 23°-26° -210"4g4 t - 0.1773 g2 t + 42.728 gt + 3433.3

8 26°-28° -0.0139g2t + 7.6375gt - 1042.7

9 28°-31° 0.0052g2t - 3.1304gt + 470.82

1° 31°-34° 0.0034g2t - 2.1686gt + 345.6

11 34°-36° 1.39

As a result of the analysis of the data given in the tables, it was found that the EPR of the HF of the BO simulator at a specific conductivity coefficient of 5.2 10-17 1/s:

According to the developed model ai = 1.428 m2;

According to the experiment, aP = 1.78 m2.

Vol. 20, no. 06, 2017

Civil Aviation High Technologies

To obtain numerical values of the EPR of the HF of the BO simulator of the developed model without taking into account the fairing, it is necessary to take into account the transmission coefficient through the fiberglass fairing, which is 3.

This is a consequence of the increased technical requirements for the radio transparency of the fiberglass fairing. Note that all the above indicatrices are rotated by an angle of 900, and the software provides for the possibility of turning the indicatrices by an angle of 90, 180, and 2700. It is also seen from these figures that the RCS of the HF simulator with and without a fairing have a similar shape and amplitude.

As a simulator of a ballistic object, a complex radar reflector made of a lossless dielectric in the form of a sphere coated with a highly electrically conductive alloy, as well as a truncated cone, a disk, and cylindrical elements was chosen. Comparative indicatrices of the simulator of ballistic objects are presented graphically.

Examples of numerical calculations of the RCS of the HF of the BO simulator with increased RCS and increased all-angle view are given, the calculation showed a high accuracy of the method, which is no more than 1-5%. The calculated indicatrices of the EPR of the variants of the HF of the BO simulator are determined.

According to the results, the variants of the warhead of the BO simulator with increased RCS and increased all-angle view with the optimal placement of the radar dielectric reflector and the corner block with sectional placement of dielectric reflectors were studied, it was shown that the all-angle view of the BO simulator increases by 2 times, and the RCS of the GS increases by 4 times. This result depends on the characteristics of the dielectric material and fiberglass, which show that the resonant frequency is 10-14 GHz, with a highly conductive coating thickness that is from 6 to 9 microns on the surface of the dielectric reflector and 15-20 microns on the surfaces of the corner block.

BIBLIOGRAPHY

1. Radio-electronic systems. Fundamentals of construction and theory: a reference book / ed. I. Shirman. M.: CJSC "Makvis", 1998. 825 p.

2. Stager E.A. Scattering of radio waves on bodies of complex shape. Moscow: Radio and communication, 1986. 183 p.

3. Makarovets N.A., Sebyakin A.Yu. Measurement of the effective scattering area of the head part of the air target simulator // Collection of abstracts of the XXIV scientific session dedicated to the Radio Day. Tula: TulGU, 2006, pp. 176-179.

5. Taflove A., Hagness S. Computational Electrodynamics: The Finite-Difference TimeDomain Method, NY, Artech House, 2000, 467 p.

6. Gibbson D. The Method of Moments in Electromagnetics. NY, Chapman & Hall CRC, 2008, 594 p.

7. Ufimtsev P.Ya. Fundamentals of the physical theory of diffraction. M.: Binom, 2009. 352 p.

8. Millimeter radar: methods of detection and guidance under natural and organized interference / A.B. Borzov [i dr.]. M.: Radiotehnika, 2010. 376 p.

9. Methods for the synthesis of geometric models of complex radar objects / A.B. Borzov [et al.] // Electromagnetic waves and electronic systems. 2003. V. 8. No. 5. S. 55-63.

10. Antifeev V.N., Borzov A.B., Suchkov V.B. Physical models of radar stray fields of objects of complex shape. M.: Publishing house of MSTU im. N.E. Bauman, 2003. 61 p.

11. ^bak V.O. Radar reflectors. M.: Secular radio. 1975. 244 p.

Civil Aviation High Technologies

Vol. 20, no. 06, 2017

12. Meizels E.N., ToproBaHoB V.A. Measurement of scattering characteristics of radar targets. Moscow: Soviet radio. 1972. 232 p.

13. Theoretical and experimental studies of the polarization characteristics of dihedral and trihedral concave structures / A.B. Borzov [et al.] // Electromagnetic waves and electronic systems. 2010. V. 15. No. 7. S. 27-40.

14. Detection of a group air target by angular noise / N.S. Akinshin, E.A. Amirbekov, R.P. Bystrov, A.V. Khomyakov // Radio engineering, 2014. No. 12. P. 70-76.

Akinshin Ruslan Nikolaevich, Doctor of Technical Sciences, Associate Professor, Leading Researcher, SPP RAS, [email protected].

Bortnikov Andrey Alexandrovich, Leading Engineer of JSC "TsKBA", [email protected].

Tsybin Stanislav Mikhailovich, Leading Engineer of JSC "TsKBA", [email protected].

Mamon Yury Ivanovich, Doctor of Technical Sciences, Chief Specialist of TsKBA JSC, [email protected].

Minakov Evgeny Ivanovich, Doctor of Technical Sciences, Associate Professor, Professor of Tula State University, [email protected].

MODEL AND ALGORITHM FOR CALCULATION OF THE RADAR SIMULATOR OBJECT EFFECTIVE SQUARE OF SCATTERING

Ruslan N. Akinshin1, Andrey A. Bortnikov2, Stanislav M. Tsibin2, Yuri I. Mamon2, Evgenii I. Minakov3

1SSP RAS, Moscow, Russia 2CDBAE, Tula, Russia 3Tula state University, Tula, Russia

Then reduce the cost of field tests of the ballistic objects (BO) simulators reflection properties, it is advisable to develop a model and algorithm for calculation of the radar objects effective surface scattering. As a simulator of ballistic objects a complex radar reflector, made of a lossfree dielectric is chosen. It looks like a spherical Luneburg lens with a coating of high-conductivity alloy as well as a truncated cone, disk, and cylindrical elements. The stages of aperture version of reflection from the inner surface of the Luneburg lens are proposed. A physical model of the reflection on the elements of design and the technique of modeling with a calculation algorithm of the effective surface scattering are developed. The algorithm of calculation of the ballistic objects resonance effective surface scattering is worked out. This algorithm is presented in a graphical form. The interface of the computing complex is presented. As a simulator of ballistic object we selected a complex radar reflector, made of a lossfree dielectric sphere with a coating of high-conductivity alloy as well as of a truncated cone, disk, and cylindrical elements. The comparative indicators of ballistic objects simulator are presented. The conclusion on the comparative analysis of the results of measurements in situ and modeling results is made. The examples of numerical calculations of the ESR of the head part of the BO simulator with increased ESR and increased all-aspect view are given. The options of the BO simulator head parts with increased ESR and increased all-aspect view with optimal placement of radar dielectric reflector and a corner unit with sectional placement of dielectric reflectors are analyzed.

Key words: effective surface scattering, ballistic object, radar reflector.

1. Radioelectronic systems. Basic construction. Reference book. M., Joint-Stock Company "Makvis", 1998, 825 p. (in English)

Vol. 20, no. 06, 2017

Civil Aviation High Technologies

2 Stager E.A. Rasseyanie radiovoln na telach slozhnoy formy. M., Radio and Communication, 1986, 183 p. (in English)

3. Makarovets N.A., Sebyakin A.Yu. Izmerenie effektivnoy ploschadi rasseyaniya golovnoy chasti imitatora vozdushnoy tseli. . Tula, Tula State University, 2006, pp. 176-179. (in English)

4 Sullivan D.M. Electromagnetic Simulation Using the FDTD Method. NY, IEEE Press, 2000, 165 p.

5. Taflove A., Hagness S. Computational Electrodynamics: The Finite-Difference TimeDomain Method. NY, Artech House, 2000, 467 p.

6. Gibbson D. The Method of Moments in Electromagnetics. NY, Chapman & Hall CRC, 2008, 594 p.

7. Ufimtsev P.Ya. Osnovy fizicheskoy theorii difraktsii. M., Binom, 2009, 352 p. (in English)

8. Millimetrovaya radiolokatsiya: metody obnaruzheniya I navedeniya v usloviyah estestvennyh I organized pomeh. A.B. Borzov. M., Radiotekhnika, 2010, 376 p. (in English)

9. Metody sinteza geometricheskih modeley slozhnyh radiolokatsionnyh ob "ektov. A.B. Borzov. Elektromagnitnye volny I elektronnye sistemy, 2003, No. 5, pp. 55-63. (in Russian)

10. Antifeyev V.N., Borzov A.B., Suchkov V.B. Fizicheskie modeli radiolokatsionnyh poley rasseyaniya ob "ektov slozhnoy formy. M., MSTU n. N.E. Bauman, 2003, 61 p. (in Russian)

11. Kobak V.O. Radiolocatsionnye reflections. M., Soviet radio, 1975, 244 p. (in English)

12. Maisels E.N., Torgovanov V.A. Izmerenie harakteristik rasseyaniya radiolokatsionnyh tseley. M., Soviet radio, 1972, 232 p. (in English)

13. Teoreticheskie i eksperimentalnye issledovaniya polyarizatsionnyh harakteristik dvugran-nyh struktur. Borzov A.B. . Elektromagnitnye volny i elektronnye sistemy. Radiotechnika, 2014, no. 12, pp.70-76. (in English)

INFORMATION ABOUT THE AUTHORS

Ruslan N. Akinshin, Doctor of Technical Sciences, Associate Professor, Senior Researcher of SPP of RAS, [email protected].

Andrey A. Bortnikov, Leading Engineer of JSC TsKBA, [email protected].

Stanislav M. Tsibin, Leading Engineer of JSC TsKBA, [email protected].

Yury I. Mamon, Doctor of Technical Sciences, Chief Specialist of JSC TsKBA, [email protected].

The dependence of the EPR of the plate on the angle formula. Effective scattering area. EPR of common point targets

Effective target scattering area (ESR).

Complex and group goals

EPR of common point targets

convex surface

flat plate

Corner reflector

Triangular

Application of corner reflectors

chaff

EPR of complex targets

EPR calculation

The physical meaning of epr

EPR of common point targets

convex surface

annotation scientific article on electrical engineering, electronic engineering, information technology, author of scientific work - Akinshin Ruslan Nikolaevich, Bortnikov Andrey Alexandrovich, Tsybin Stanislav Mikhailovich, Mamon Yuri Ivanovich, Minakov Evgeny Ivanovich

Related Topics scientific papers on electrical engineering, electronic engineering, information technology, author of scientific work - Akinshin Ruslan Nikolaevich, Bortnikov Andrey Alexandrovich, Tsybin Stanislav Mikhailovich, Mamon Yuri Ivanovich, Minakov Evgeny Ivanovich

The text of the scientific work on the topic "Model and algorithm for calculating the effective scattering area of ​​a simulator of a radar object"

The text of the scientific work on the topic "Model and algorithm for calculating the effective scattering area of a simulator of a radar object"